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John Derbyshire

Unknown Quantity

X: The unknown quantity. But how did the idea of using letters to represent numbers in this way originate. That's one of the questions that John Derbyshire investigates in Unknown Quantity A Real and Imaginary History of Algebra. He looks at the work of early writers such as Diophantus, and describes how the development of the subject continued in the Arabic world. The book then moves on to the work done following the Renaissance in Europe, and in particular the solution of polynomial equations of one variable, leading to the work of Abel and Galois showing the insolubility of the quintic.

The second half of the book gets onto more recent developments in algebra, in particular the tendency towards abstraction which followed the work of Galois. Derbyshire looks at the origin of structures such as groups, fields, rings, vector spaces and many others.

The book has more maths in it than many of its type, but it shouldn't pose any problem to those with a reasonable grasp of high-school mathematics. This has the advantage that it gives a more complete description of the work done on solving equations, and the later parts give a useful taster of what is taught in university mathematics courses.

Amazon.com info
Paperback 374 pages  
ISBN: 0452288533
Salesrank: 497550
Weight:0.75 lbs
Published: 2007 Plume
Amazon price $11.34
Marketplace:New from $5.05:Used from $2.97
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Amazon.co.uk info
Paperback 400 pages  
ISBN: 0452288533
Salesrank: 2149530
Weight:0.75 lbs
Published: 2007 Plume Books
Marketplace:New from £8.84:Used from £2.88
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Amazon.ca info
Paperback 400 pages  
ISBN: 0452288533
Salesrank: 271789
Weight:0.75 lbs
Published: 2007 Plume
Amazon price CDN$ 19.31
Marketplace:New from CDN$ 12.27:Used from CDN$ 6.35
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Product Description
For curious nonmathematicians and armchair algebra buffs, John Derbyshire discovers the story behind the formulae, roots, and radicals. As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel?s proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from ?this plus this equals this? to ?this plus what equals this?? gave birth to a whole new way of perceiving the world. With a historian?s narrative authority and a beloved teacher?s clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging journey through the development of abstract mathematical thought.